ChemistryAngular momentumUniversity
Angular momentum component commutator Calculator
Shows that different angular-momentum components do not commute.
Use the free calculatorCheck the variablesOpen the advanced solver
Formula first
Overview
Only one component of angular momentum can be specified sharply together with the total magnitude.
Apply it well
When To Use
When to use: Shows that different angular-momentum components do not commute.
Why it matters: Only one component of angular momentum can be specified sharply together with the total magnitude.
Avoid these traps
Common Mistakes
- Assuming Lx, Ly, and Lz can all be known exactly together.
- Dropping the factor of i hbar.
One free problem
Practice Problem
What is [Lx, Ly] using the angular-momentum commutator?
Solve for: $[\hat{L}_i, \hat{L}_j]
Hint: Focus on what the formula is telling you physically.
The full worked solution stays in the interactive walkthrough.
References
Sources
- Chemistry LibreTexts, Rotational Motions of Rigid Molecules; Chemistry LibreTexts, Selection Rule for the Rigid Rotator
- Chemistry LibreTexts, Rotational Motions of Rigid Molecules
- Chemistry LibreTexts, Selection Rule for the Rigid Rotator
- NIST CODATA
- IUPAC Gold Book
- Quantum Mechanics, by David J. Griffiths
- Principles of Quantum Mechanics, by R. Shankar
- Griffiths, David J. Introduction to Quantum Mechanics